Top of pageAbstractThe reliable detection of single quantum particles has revolutionized the field of quantum optics and quantum information processing. For several years, researchers have aspired to extend such detection possibilities to larger-scale, strongly correlated quantum systems1, 2 in order to record in situ images of a quantum fluid in which each underlying quantum particle is detected. Here we report fluorescence imaging of strongly interacting bosonic Mott insulators in an optical lattice with single-atom and single-site resolution. From our images, we fully reconstruct the atom distribution on the lattice and identify individual excitations with high fidelity. A comparison of the radial density and variance distributions with theory provides a precise in situ temperature and entropy measurement from single images. We observe Mott-insulating plateaus with near-zero entropy and clearly resolve the high-entropy rings separating them, even though their width is of the order of just a single lattice site. Furthermore, we show how a Mott insulator melts with increasing temperature, owing to a proliferation of local defects. The ability to resolve individual lattice sites directly opens up new avenues for the manipulation, analysis and applications of strongly interacting quantum gases on a lattice. For example, one could introduce local perturbations or access regions of high entropy, a crucial requirement for the implementation of novel cooling schemes3.